Mathematical Sciences: Cyclic Homology and D-Modules

本研究项目涉及几个上同调理论（循环上同调、等变上同调、椭圆上同调）和d模的几何方面及其应用。重要代数（微分和伪微分算子，李群的群代数，交叉积代数）的循环同调将进一步研究，并与几何，拓扑和表示理论中的问题相关。这包括具有等变上同调的关系，它将应用于李群在流形上的作用。研究者将研究椭圆上同调的几何和数论方面。他还将探讨与Hodge理论和曲线模空间有关的d模的几个难题。

This research project concerns the geometrical aspects and applications of several cohomology theories (cyclic homology, equivariant cohomology theories, elliptic cohomology), and also D-modules. The cyclic homology of important algebras (differential and pseudo-differential operators, group algebras for Lie groups, crossed-product algebras) will be further studied and related to problems in geometry, topology, and representation theory. This includes relations with equivariant cohomology, which will be applied to actions of Lie groups on manifolds. The investigator will study the geometric and number-theoretic aspects of elliptic cohomology. He will also pursue several difficult questions on D-modules in relation to Hodge theory and moduli spaces of curves.